Inductive Structures in Mathematical Physics: A Historical and Methodological Perspective

Mathematical physics is the discipline of applying rigorous mathematical methods to problems in physics. In this paper, we argue that many techniques used in mathematical physics inherently follow the logical structure of mathematical induction. We present historical evidence that the development of mathematical physics methodologies has been guided by inductive patterns, a formal proof illustrating the inductive nature of these methods, and examples from physics that demonstrate this inductive principle in action. We discuss the implications of viewing mathematical physics through the lens of induction, suggesting that this perspective highlights the rigor and generality of physical laws. Finally, we conclude with a summary of findings and propose directions for future research in both the philosophy and education of mathematical physics.